About magnetization in ferromagnetic material I am studying about ferromagnetism and have wondered whether the magnetization can be aligned independently of external magnetic field direction.
As far as I know, the ferromagnetic material has no linear relationship between magnetization M and external magnetic field H, thus I guess there is no need that M doesn't have to be parallel with H.
But in many figures, when an external field is applied, the all spins are aligned parallel with that of an external field as you  can see below:

So, I'm confused whether the magnetization doesn't have to follow the direction of the external field or not.
Please help me out.
 A: Above the critical temperature such a material exhibits paramagnetic properties, i.e. the spins align along the magnetic field. However, below the critical temperature it is in a ferromagnetic phase, which a specific value of the magnetization. Changing the direction of this magnetization than requires applying a sufficiently strong field - hence the non-unique dependence of the magnetization on the applied field in the magnetization curves.
A: In non-magnetized piece of ferromagnetic material, the atomic dipoles in each domain tend to align their dipole moments with the randomly oriented crystal axes. The shape and size of the crystal can also be a factor in determining the configuration with minimum energy. In an external field, the dipoles swing toward the external field with the amount of swing depending on the strength of the field. The resultant magnetization will tend to align with the field, but can be affected by the shape of the ferromagnet.  During this process, some of the domain moments may be reversed, thus leaving a remnant magnetization when the external field is removed.  If a new external field is applied which is not in line with the remnant, the resulting magnetization will not at first be in line with the new field.
